Dynamical effects of the cosmological constant

Abstract

The possibility of measuring the density parameter Ω0 and the cosmological constant |$\lambda_0 \equiv\Lambda/(3H^{2}_{0})$| using dynamical tests is explored in linear and non-linear theory. In linear theory we find that the rate of growth of the perturbations at the present epoch is approximated by |$f(z = 0) \approx \Omega^{0.6}_{0}+ \frac1{70} \lambda_0(1+ \frac1{2} \Omega_0)$|⁠. Therefore, dynamical tests such as infall around clusters and dipoles at the present epoch do not distinguish well between universes with and without a cosmological constant. At higher redshifts, the perturbations also depend mainly on the matter density at a particular epoch, |$f(z) \approx \Omega^{0.6}(z)$|⁠, which has a strong dependence on λ0 at |$z \approx 0.5-2.0$|⁠. Therefore, information on both parameters can be obtained by looking at clustering at different redshifts. In practice, however, the other observables also depend on the cosmology, and in some cases conspire to give a weak dependence on λ0. By using the non-linear spherical infall model for a family of Cold Dark Matter (CDM) power-spectra we also find that dynamics at z = 0 does not tell much about λ0. At higher redshifts there is unfortunately another conspiracy between conventional observables, which hides information about λ0. The final radius of a virialized cluster (relative to the turn-around radius) is approximated by |$R_\text{f}/R_\text{ta} \approx (1-\eta/2)/(2-\eta/2)$|⁠, where η is the ratio of Λ to the density at turn-around. Therefore a repulsive Λ gives a smaller final radius than a vanishing Λ.